By Thomas A. Ivey
This booklet is an advent to Cartan's method of differential geometry. valuable equipment in Cartan's geometry are the idea of external differential structures and the strategy of relocating frames. This ebook provides thorough and smooth remedies of either topics, together with their purposes to either vintage and modern difficulties. It starts with the classical geometry of surfaces and simple Riemannian geometry within the language of relocating frames, besides an hassle-free creation to external differential structures. Key strategies are constructed incrementally with motivating examples resulting in definitions, theorems, and proofs. as soon as the fundamentals of the equipment are tested, the authors improve functions and complicated topics.One impressive program is to complicated algebraic geometry, the place they extend and replace vital effects from projective differential geometry. The booklet gains an advent to $G$-structures and a remedy of the idea of connections. The Cartan equipment can be utilized to procure specific options of PDEs through Darboux's process, the tactic of features, and Cartan's approach to equivalence. this article is acceptable for a one-year graduate path in differential geometry, and elements of it may be used for a one-semester path. It has a number of workouts and examples all through. it is going to even be precious to specialists in parts equivalent to PDEs and algebraic geometry who are looking to find out how relocating frames and external differential platforms practice to their fields.